x=a(-sin), y=a(1-cos).... What?A few days ago, I met an old post about Cycloid in Revit from Aaron's "Malleristic Revitation". It was a really mind blowing post. After reading it, I just thought that what if a real wheel can be rolled on a string? It must be much easier to get a cycloid shape if it's possible. So I tried as below.
1. A Rolling Wheel
At the above picture, it's easy to know that Position1 on a straight line and Position2 on a circle have to be associated each other when it rolled. It means Normalized Cuve Parameter of both points are same on both hosts; line & circle. (Actually it can be a little different)
2. RepeaterTo get enough points, I created a 3pt circle family which can detect line length and Position1. It will resize the circle and relocate Position2 automatically with repeater.
3. "The Helen of Geometry"
Now, you can get your fine Cycloid here.
I can't say it's a better way than Aaron's, but quite sure it's an 'easier' way.
Thanks for your clever modeling and great posts, Aaron.